Minimal Controllability of Sphere and Torus Grid Graphs

IF 7 1区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

IEEE Transactions on Automatic Control Pub Date : 2026-10-01 Epub Date: 2026-06-01 DOI:10.1109/TAC.2026.3698015

Tianhao Li;Yibei Li;Zhixin Liu;Xiaoming Hu

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Abstract

Network controllability is essential for designing the control algorithms of networked systems, among which the minimal controllability problem has attracted much attention of researchers due to the need of conserving control resources in practical applications. In this article, we investigate the minimal controllability problem of Laplacian dynamics on two classes of nonplanar graphs, namely, sphere grid graphs and torus grid graphs. Since the Laplacian matrices of sphere grid graphs are closely related to the adjacency matrices of cylinder grid graphs, we first analyze the minimal numbers of control nodes required to guarantee controllability of networked linear systems whose system matrices are adjacency matrices of cylinder grid graphs. By exploring the relation between Laplacian matrices of sphere grid graphs and adjacency matrices of cylinder grid graphs, we then establish upper and lower bounds for the minimal number of control nodes required to guarantee controllability of Laplacian dynamic systems on sphere grid graphs. Finally, we provide the exact minimal number of control nodes and a corresponding control node set to guarantee controllability of the Laplacian dynamic systems on torus grid graphs.

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球面和环面网格图的最小可控性

网络的可控性是设计网络系统控制算法的关键，其中最小可控性问题由于在实际应用中需要节约控制资源而备受关注。本文研究了两类非平面图即球面网格图和环面网格图上拉普拉斯动力学的最小可控性问题。由于球面网格图的拉普拉斯矩阵与柱面网格图的邻接矩阵密切相关，我们首先分析了以柱面网格图的邻接矩阵为系统矩阵的网络线性系统保证可控性所需的最小控制节点数。通过探索球面网格图的拉普拉斯矩阵与圆柱网格图的邻接矩阵之间的关系，建立了保证球面网格图上拉普拉斯动态系统可控所需的最小控制节点数的上界和下界。最后，我们给出了精确的最小控制节点数和相应的控制节点集，以保证环面网格图上拉普拉斯动态系统的可控性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Automatic Control 工程技术-工程：电子与电气

CiteScore

11.30

自引率

5.90%

发文量

824

审稿时长

9 months

期刊介绍： In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered: 1) Papers: Presentation of significant research, development, or application of control concepts. 2) Technical Notes and Correspondence: Brief technical notes, comments on published areas or established control topics, corrections to papers and notes published in the Transactions. In addition, special papers (tutorials, surveys, and perspectives on the theory and applications of control systems topics) are solicited.